Найти интеграл? 5 заданий решите пожалуйста

[latex]1)\; \; \frac{cos^2t-ctg^2t}{sin^2t-tg^2t}=\frac{cos^2t-\frac{cos^2t}{sin^2t}}{sin^2t-\frac{sin^2t}{cos^2t}}=\frac{cos^2t(sin^2t-1)}{sin^2t(cos^2t-1)}=\frac{cos^2t(-cos^2t)}{sin^2t(-sin^2t)}=\\\\=\frac{cos^4t}{sin^4t}=ctg^4t[/latex] [latex]2)\; \; \frac{(sinx+cosx)^2-1}{tgx-sinx\cdot cosx}=\frac{1+2sinx\cdot cosx-1}{\frac{sinx}{cosx}-sinx\cdot cosx}=\frac{2sinx\cdot cos^2x}{sinx(1-cos^2x)}=\\\\=\frac{2cos^2x}{sin^2x}=2ctg^2x\\\\3)\; \; \frac{ctgx}{tgx+ctgx}=\frac{cosx}{sinx\cdot (\frac{sinx}{cosx}+\frac{cosx}{sinx})}=\frac{cosx\cdot sinx\cdot cosx}{sinx(sin^2x+cos^2x)}=\frac{cos^2x}{1} =cos^2x[/latex]